Determine the intercepts of the line x/y -6,-10 -4,-6 -2,-2 with table values

Step-by-step explanation:

The two-point form of the equation of a line can be used to start:

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (-6 -(-10))/(-4 -(-6))(x -(-6)) +(-10)

  y = 4/2(x +6) -10

  y = 2x +2

When x=0, y = 2. When y=0, x=-1.

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This is consistent with our observation that x-values in the table increase by 2 while y-values increase by 4. The next table entry in that pattern will be ...

  (x, y) = (-2 +2, -2 +4) = (0, 2) . . . . the y-intercept

We note that this point and the previous one (-2, -2) have y-values symmetrically located about y=0. Hence the corresponding x-value will be the average of the x-values:

  (x, y) = ((0, 2) +(-2, -2))/2 = (-1, 0) . . . . the x-intercept